A High Performance Dual Revised Simplex Solver

Hall, Julian; Huangfu, Qi

doi:10.1007/978-3-642-31464-3_15

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…Two other valuable attempts are presented in [26][27] following the primal-dual simplex method and the sparse simplex method, and they've led to satisfactory results for large scale problems. Till recently, no other valuable attempts have been made to parallelize the classical revised simplex method, thus making the one presented by Huangfu and Hall [28][29] a distinguished one. The authors in [28][29] have designed and implemented a very efficient parallelization scheme of the dual revised method with use of the suboptimization technique, and they have obtained speedup values comparable to those of the best commercial simplex solvers.…”

Section: Related Workmentioning

confidence: 99%

“…Till recently, no other valuable attempts have been made to parallelize the classical revised simplex method, thus making the one presented by Huangfu and Hall [28][29] a distinguished one. The authors in [28][29] have designed and implemented a very efficient parallelization scheme of the dual revised method with use of the suboptimization technique, and they have obtained speedup values comparable to those of the best commercial simplex solvers. A relevant survey which covers adequately all the recent advances in simplex parallelization can be found in [12].…”

Section: Related Workmentioning

confidence: 99%

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Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

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Abstract-The simplex method has been successfully used in solving linear programming (LP) problems for many years. Parallel approaches have also extensively been studied due to the intensive computations required, especially for the solution of large LP problems. Furthermore, the rapid proliferation of multicore CPU architectures as well as the computational power provided by the massive parallelism of modern GPUs have turned CPU / GPU collaboration models increasingly into focus over the last years for better performance. In this paper, a highly scalable implementation framework of the standard full tableau simplex method is first presented, over a hybrid parallel platform which consists of multiple multicore nodes interconnected via a high-speed communication network. The proposed approach is based on the combined use of MPI and OpenMP, adopting a suitable column-based distribution scheme for the simplex tableau. The parallelization framework is then extended in such a way that it can exploit concurrently the full power of the provided resources on a multicore single-node environment with a CUDA-enabled GPU (i.e. using the CPU cores and the GPU concurrently), based on a suitable hybrid multithreading/GPU offloading scheme with OpenMP and CUDA. The corresponding experimental results show that the hybrid MPI+OpenMP based parallelization scheme leads to particularly high speed-up and efficiency values, considerably better than in other competitive approaches, and scaling well even for very large / huge linear problems. Furthermore, the performance of the hybrid multithreading/GPU offloading scheme is clearly superior to both the OpenMP-only and the GPU-only based implementations in almost all cases, which validates the worth of using both resources concurrently. The most important, when it is used in combination with MPI in a multi-node (fully hybrid) environment, it leads to substantial improvements in the speedup achieved for large and very large LP problems.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

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“…Although applicable in general, all are motivated by the requirements of the high performance implementation by Hall and Huangfu [1,15] of the dual revised simplex method with suboptimization introduced by Rosander [18].…”

Section: New Update Techniquesmentioning

confidence: 99%

“…The opportunities and limitations of modern computer architectures, together with the desire to solve ever larger problem instances, continue to drive developments in high performance computing techniques for the simplex method [1,2].…”

Section: Introductionmentioning

confidence: 99%

Novel update techniques for the revised simplex method

Huangfu

Hall

2014

Comput Optim Appl

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This paper introduces three novel techniques for updating the invertible representation of the basis matrix when solving practical sparse linear programming problems using a high performance implementation of the dual revised simplex method, being of particular value when suboptimization is used. Two are variants of the product form update and the other permits multiple Forrest-Tomlin updates to be performed. Computational results show that one of the product form variants is significantly more efficient than the traditional approach, with its performance approaching that of the Forrest-Tomlin update for some problems. The other is less efficient, but valuable in the context of the dual revised simplex method with suboptimization. Results show that the multiple Forrest-Tomlin updates are performed with no loss of serial efficiency.

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“…The fundamental design of pami was introduced by Hall and Huangfu [7], where it was referred to as ParISS. This prototype implementation was based on the PF update and was relatively unsophisticated, both algorithmically and computationally.…”

Section: Parallelism Across Multiple Iterationsmentioning

confidence: 99%

Parallelizing the dual revised simplex method

Huangfu¹,

Hall

2017

Math. Prog. Comp.

127

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This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational components when possible. Computational results show that the performance of PAMI is superior to that of the leading open-source simplex solver, and that SIP complements PAMI in achieving speedup when PAMI results in slowdown. One of the authors has implemented the techniques underlying PAMI within the FICO Xpress simplex solver and this paper presents computational results demonstrating their value. In developing the first parallel revised simplex solver of general utility, this work represents a significant achievement in computational optimization.

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A High Performance Dual Revised Simplex Solver

Cited by 8 publications

References 16 publications

Simplex Parallelization in a Fully Hybrid Hardware Platform

Simplex Parallelization in a Fully Hybrid Hardware Platform

Novel update techniques for the revised simplex method

Parallelizing the dual revised simplex method

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